There is plenty of evidence that adaptive designs make statistics non-normally distributed. [1]} point out that the distribution of stage-specific test statistics is not normal and should be estimated recursively. [2]} plot the density of a normal test statistic used in GSD settings [pages 174-177], where discontinuity points clearly show non-normality. [3]} find the joint density of stage 1 and stage 2 standardized test statistics not to be bivariate normal. Local asymptotic non-normality was established following sample size recalculations (SSRs) that depend on an interim observed treatment effect ([4]}, [5]}); and a GSD with a single interim analysis can be viewed as a special case of an SSR. MLEs converging to random mixtures of normal variables have been found in other adaptive designs ([6]}, [7]}, [8]}, [9]},
[10]}).
